Problem: $\dfrac{ 10w - 10x }{ -6 } = \dfrac{ 9w + 3y }{ 2 }$ Solve for $w$.
Explanation: Multiply both sides by the left denominator. $\dfrac{ 10w - 10x }{ -{6} } = \dfrac{ 9w + 3y }{ 2 }$ $-{6} \cdot \dfrac{ 10w - 10x }{ -{6} } = -{6} \cdot \dfrac{ 9w + 3y }{ 2 }$ $10w - 10x = -{6} \cdot \dfrac { 9w + 3y }{ 2 }$ Reduce the right side. $10w - 10x = -{6} \cdot \dfrac{ 9w + 3y }{ {2} }$ $10w - 10x = -{3} \cdot \left( 9w + 3y \right)$ Distribute the right side $10w - 10x = -{3} \cdot \left( {9w} + {3y} \right)$ $10w - 10x = -{27}w - {9}y$ Combine $w$ terms on the left. ${10w} - 10x = -{27w} - 9y$ ${37w} - 10x = -9y$ Move the $x$ term to the right. $37w - {10x} = -9y$ $37w = -9y + {10x}$ Isolate $w$ by dividing both sides by its coefficient. ${37}w = -9y + 10x$ $w = \dfrac{ -9y + 10x }{ {37} }$